Reordered exposition for H

Author: SubjunctiveQuaver

_posts/2026-01-05-algebraist-field-guide.md

@@ -225,7 +225,7 @@ Define the subring $\mathcal{C}(\mathbb{Q}) \subseteq \mathbb{Q}^{\infty}$ consi
 
 Inside $\mathcal{C}(\mathbb{Q})$, define the ideal of null sequences:[^3]
 
-[^3]: An ideal $I$ is a special subset of a ring, itself closed under addition and 'absorbs' multiplication by any element of the ring. Ideals allow us to form quotient rings, which generalise the idea of modular arithmetic.
+[^3]: An ideal is a special subset of a ring, itself closed under addition and 'absorbs' multiplication by any element of the ring. Ideals allow us to form quotient rings, which generalise the idea of modular arithmetic.
 
 $$\mathcal{N}(\mathbb{Q}) = \{ (x_n) \in \mathcal{C}(\mathbb{Q}) : x_n \to 0 \text{ as } n \to \infty \}$$
 
@@ -343,9 +343,9 @@ We're getting to a point where it's getting harder to justify the existence of n
 
 Later in 1877, Ferdinand Georg Frobenius showed that the quaternions are one of only 3 associative division algebras over the reals (the others being $\mathbb{R}$ and $\mathbb{C}$). This result was extended by Adolf Hurwitz, who classified normed division algebras, showing that the only normed division algebras over the reals are $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and the octonions $\mathbb{O}$.
 
-**In real life:** Quaternions are used in 3D computer graphics and robotics to represent rotations. A unit quaternion acts on 3‑dimensional space by conjugation, avoiding issues like gimbal lock that can occur with Euler angles.[^2]
+**In real life:** Quaternions are used in 3D computer graphics and robotics to represent rotations. A unit quaternion acts on 3‑dimensional space by conjugation, avoiding issues like gimbal lock that can occur with Euler angles.[^2] (I might write a separate post on this later.)
 
-[^2]: A 3D rotation by a unit quaternion $q \in S^3$ acts on a vector $v \in \operatorname{Im}(\mathbb{H}) \cong \mathbb{R}^3$ via the map $v \mapsto qvq^{-1}$. (I might write a separate post on this later.)
+[^2]: A 3D rotation by a unit quaternion $q \in S^3$ acts on a vector $v \in \operatorname{Im}(\mathbb{H}) \cong \mathbb{R}^3$ via the map $v \mapsto qvq^{-1}$.
 
 ### ℍ: Construction